I loaded up a bunch of tankers and disbanded them a couple turns back. Seems like they were perfectly fine at that time. Now several of them have like 9 to 12 Sys damage, despite having sat in port for only a couple days with fuel in them. Is this wear and tear, and if so: is this realistic!?!

Like a tanker cannot fill up then just sit there at dock indefinitely without causing any sys damage!?

Helpless is right. At the start of the scenario, the human player has to manually turn off the upgrade toggle on all the ships in a port with a repair yard or they'll dump into a refit queue. Beware that on January 1, 1927 almost all of your US destroyers will do the same thing if they're in a port with a yard.